An engine unit of a conventional engine-driven working machine has a crankcase and a crankshaft, and the crankshaft includes a drive-side shaft extending from a drive side of the crankcase and a magnet-side shaft extending from a magnet side of the crankcase. Further, oil seals for ensuring airtightness in the engine unit are provided between the crankcase and the drive-side and magnet-side shafts. Further, a vaned rotor (for example, a vaned flywheel) is attached to the magnet-side shaft, and rotations of the vaned rotor cause an airflow for cooling the engine unit (especially a cylinder block with fines in an upper portion of the engine unit) (see, for example, Patent Publication 1).